EP0879443B1 - Methode zum optimalreglerentwurf für eine voraussagende mehrgrössensteuerung mit hilfe einer messbereichsteuerung - Google Patents
Methode zum optimalreglerentwurf für eine voraussagende mehrgrössensteuerung mit hilfe einer messbereichsteuerung Download PDFInfo
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- EP0879443B1 EP0879443B1 EP96912528A EP96912528A EP0879443B1 EP 0879443 B1 EP0879443 B1 EP 0879443B1 EP 96912528 A EP96912528 A EP 96912528A EP 96912528 A EP96912528 A EP 96912528A EP 0879443 B1 EP0879443 B1 EP 0879443B1
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- variables
- controller
- control
- robust
- parameters
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
- G05B13/048—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators using a predictor
Definitions
- the present invention relates to control systems, and more particularly, to a method of designing an optimal controller for robust multivariable predictive control (RMPC) techniques utilizing range controls.
- RMPC multivariable predictive control
- US Patent 5 351 184 discloses a process control system with at least one manipulated variable and at least one controlled variable for robust control of a process.
- the present invention provides a method for providing the robust control of a process, the method as defined Claim 1 hereinafter.
- a process control system which includes at least one manipulated variable and at least one controlled variable, provides a method for robust control of a process. Predetermined constraints of the manipulated variables and the controlled variables, and the present values of the manipulated variables and the controlled variables, and the present values of the manipulated variables are obtained.
- the controller is loaded with parameters which define an optimal controller, the parameters being calculated off-line. To determine the parameters a single min-max statement is defined for a worst case model of the process which operates in conjunction with a best case controller.
- the single min-max statement is converted to a corresponding canonical expression in the form of a minimization problem, the resultant solution of the minimization problem being the parameter.
- New values are calculated for the controlled variables for a predetermined number of points in the future, such that the values of the controlled variables are within the predetermined range thereby obtaining an optimal robustness of the resultant controller.
- the manipulated variables are also calculated to be within predetermined constraints, and the controlled variables to fall within a predetermined range when controllable. From a plurality of solutions, a most robust solution is selected. Then the manipulated variables are adjusted to cause the process control system to driver the values of the controlled variables to the calculated values.
- a method of designing a controller of a process system of multivariable predictive control utilizing range control is designed to operate a process, the process being worst case.
- the controller is designed to operate a process, the process being worst case.
- an optimal controller for the process is achieved, and in the event the actual process is not a worst case process, the controller performance is better than anticipated.
- the present invention may provide a method of determining a best controller to achieve optimal control performance on a worst case process system.
- Figure 1 shows a functional block diagram of a process control system in which the present invention may be utilized.
- a controller 10 has multiple outputs, which are coupled as input variables u to a process 20.
- the process 20 can include, for example, a plurality of elements which can be controlled such as valves, heaters,....
- Process variables y of process 20 include temperature, pressure, level, flow,... which govern product quality.
- the input variables (or manipulated variables) u are defined as: and the output variables (or controlled variables) cv, are defined as:
- the process 20 is a dynamic process P(m), having k manipulated variables and n controlled variables.
- the controlled variables (cv) include n 1 regulated cv, n 2 restrained cv, and n 3 optimized cv.
- the range control function of controller 10 is formulated to handle the three cases identified above and is fully described in U.S. Patent 5,351,184, identified above.
- the robust control design insures both robust stability and robust performance.
- the former insures that the controller is stable for all plants in the set characterized by the uncertainty, while the later insures that reasonable performance can be expected for the same set of plants.
- the optimal robust control design problem in general form is: which states the problem is to find a controller Q that minimizes the worst performance J over all parameters m.
- the performance J is invariably a complex function involving the controller Q 10, the process P 20, and the model M 30. Stability and performance issues further constrain the design.
- model uncertainty constrains the maximum singular value of the complementary sensitivity function.
- the robust performance requirement constrains the design through the structured singular value.
- robust control design seeks to solve the min-max problem directly for the controller Q 10. Since constraint handling is the most important aspect of virtually all industrial process controllers, conventional robust design is not directly applicable. There are, however, two critical robust control concepts that are instrumental in formulating the RMPC design. The first is the use of the maximum singular value to establish norm bounds on the RMPC controller which is fully described in the patent identified above. The second is the use of the min-max principle for controller synthesis and is discussed below.
- the process P (m) 20 is parameterized, e.g., gain, time constant, time delay (or deal time), which are unknown but defined such that a parameter m is between a high and low bound.
- the model M 30 is a "description" of the process P 20, however, there is often some degree of mismatch between the model 30 and the process 20.
- the RMPC controller can be determined (as described by a range control algorithm [RCA] in the aforementioned patent). Because of the mismatch between the model and the process, different variables are used.
- the process P is defined in terms of m
- the model M is defined in terms of p.
- the problem to be solved by the present invention is:
- the canonical form can be shown to be equivalent by graphical interpretation.
- the canonical form is much easier to solve, since this is a minimization problem.
- Any point p A drawn in the function domain can be mapped in a function space.
- J i is a function of p, and m 1 , resolves into J 1 and m 2 resolves into J 2 .
- All the points within the function domain map into some shape (shown in the function space as an ellipse for example purposes only. Now find the point X because this results in the smallest value of J 1 , J 2 .
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- Engineering & Computer Science (AREA)
- Health & Medical Sciences (AREA)
- Artificial Intelligence (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Evolutionary Computation (AREA)
- Medical Informatics (AREA)
- Software Systems (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Automation & Control Theory (AREA)
- Feedback Control In General (AREA)
Claims (1)
- Verfahren zum Bereitstellen der robusten Regelung eines Prozesses in einem Prozeßregelsystem mit einem Regler (10) zum Bereitstellen einer robusten Regelung für einen Prozeß, wobei der Prozeß ferner mindestens eine manipulierte Variable (u) und mindestens eine Prozeßvariable (cv) aufweist, gekennzeichnet durch die folgenden Schritte:a) Laden von Parametern in den Regler, die einen optimalen Regler definieren, wobei die Parameter off-line berechnet werden, mit den folgenden Schritten:i) Definieren einer einzigen Min-Max-Anweisung für ein Modell des ungünstigsten Falls des Prozesses zur Zusammenwirkung mit dem Regler, der einen besten Fall hat;ii) Umsetzen der Min-Max-Anweisung in einen entsprechenden Minimierungsausdruck, wobei der entsprechende Minimierungsausdruck ein kanonischer der einzigen Min-Max-Anweisung ist; undiii) Lösen des Minimierungsproblems mit dem Ergebnis einer resultierenden Lösung, wobei es sich bei der resultierenden Lösung um die Parameter handelt;b) Initialisieren der robusten Regelung mit vorbestimmten Einschränkungen der manipulierten Variablen und der geregelten Variablen;c) Bestimmen von derzeitigen Werten der manipulierten Variablen und der Prozeßvariablen, wobei die Prozeßvariablen Meßparametern des Prozesses entsprechen;d) Berechnen neuer Werte der Prozeßvariablen für eine vorbestimmte Anzahl von Punkten in der Zukunft, damit die Werte der Prozeßvariablen in dem vorbestimmten Bereich liegen, um eine optimale Robustheit des resultierenden Reglers zu erhalten, wobei die manipulierten Variablen innerhalb vorbestimmter Einschränkungen liegen und die Prozeßvariablen in einen vorbestimmten Bereich fallen, wenn sie steuerbar sind; andernfalls Halten der Verletzungen der Einschränkungen durch die Prozeßvariablen auf einem Minimum;e) Auswählen einer robustesten Lösung von mehreren Lösungen; undf) Regeln des Prozesses gemäß der robustesten Lösung.
Applications Claiming Priority (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US08/415,881 US5572420A (en) | 1995-04-03 | 1995-04-03 | Method of optimal controller design for multivariable predictive control utilizing range control |
US415881 | 1995-04-03 | ||
PCT/US1996/004489 WO1996031813A1 (en) | 1995-04-03 | 1996-04-01 | A method of optimal controller design for multivariable predictive control utilizing range control |
Publications (2)
Publication Number | Publication Date |
---|---|
EP0879443A1 EP0879443A1 (de) | 1998-11-25 |
EP0879443B1 true EP0879443B1 (de) | 2002-06-26 |
Family
ID=23647601
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
EP96912528A Expired - Lifetime EP0879443B1 (de) | 1995-04-03 | 1996-04-01 | Methode zum optimalreglerentwurf für eine voraussagende mehrgrössensteuerung mit hilfe einer messbereichsteuerung |
Country Status (6)
Country | Link |
---|---|
US (1) | US5572420A (de) |
EP (1) | EP0879443B1 (de) |
JP (1) | JP3843128B2 (de) |
CN (1) | CN1238775C (de) |
DE (1) | DE69622047T2 (de) |
WO (1) | WO1996031813A1 (de) |
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CN1180422A (zh) | 1998-04-29 |
CN1238775C (zh) | 2006-01-25 |
JP3843128B2 (ja) | 2006-11-08 |
WO1996031813A1 (en) | 1996-10-10 |
DE69622047D1 (de) | 2002-08-01 |
DE69622047T2 (de) | 2002-12-19 |
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